We intent this time to show how the P-values are distributed when one tests the difference of mean normal Populations. To this purpose samples X~N (0, 1).n and Y~N (0, 1): n are simulated and the statistics is: T = (xhat ? yhat - D)/s__s^2 = (ssdX + ssdY)/(n+n-2) * (1/nX + 1/nY)It´s known that T follows a Student T with nX + nY - 2 df. Lacking an algorithm to provide the inverse T we switched to normal which is sufficiently accurate since the sample sizes are large, n=100, because student t with 100+100-2= 198 df is very lose to normal standard. See 26.2.10 M. Abramowitz, I. Stegun, Handbook of Mathematical Functions. A recurrence formula (program WATCH) my own, was used.

Results and Discussion

P-values are shown (not in full) distributed in classes each one 0.05 amplitude. One get only 2% *rejections* from [0, 1], and any (as expected) when D= 0. We counted 1- alpha(D= -0.5) = 37982/40000 = 0.950, 1- alpha(D= 0.5) = 37903/40000 = 0.948 very close to 0.95, as it was demanded.